# MAT 153 Precalculus

Instructor:
Office:
Office hours:
Phone:
Email:

### Course Description

Functions, including their graphs, domain, range, inverse functions. Standard algebraic transformations of functions and the corresponding geometric transformations of their graphs. Exponential and logarithmic functions and equations; exponential growth and decay. Right-triangle trigonometry and applications. Trigonometric and inverse trigonometric functions and their graphs. Harmonic motion and sinusoids. Trigonometric identities and equations. The laws of sines and cosines.

MAT 153 meets for four hours of lecture per week.

### Prerequisites

MAT 009 or equivalent.

### Objectives

After completing MAT 153 the student should be able to

• obtain the domain and graph of linear, quadratic, exponential, logarithmic, trigonometric, and inverse trigonometric functions
• understand the Vertical and Horizontal Line Tests
• find the composition of two functions algebraically, and the inverse of a function, both algebraically and geometrically
• understand the effects on the graph of a function (e.g. translations and/or reflections) due to standard algebraic changes to the function
• use laws of exponents and logarithms and trigonometric identities
• simplify expressions involving exponential, logarithmic, and trigonometric functions
• solve exponential, logarithmic, and trigonometric equations
• prove trigonometric identities
• solve standard exponential growth and decay problems
• understand the correspondence between the symmetries of the trigonometric circle and the symmetries of the trigonometric functions
• use a graphic calculator to graph and evaluate exponential, logarithmic, and trigonometric functions
• solve triangles using the Laws of Sines and Cosines
• apply trigonometry to surveying, navigation, area, and angular speed problems and harmonic oscillations
• throughout, use standard mathematical notation and terminology and avoid nonsensical expressions and statements.

### Expected outcomes

Students should be able to demonstrate through written assignments, tests, and/or oral presentations, that they have achieved the objectives of MAT 153.

### Method of Evaluating Outcomes

Evaluations are based on homework, class participation, short tests and scheduled examinations covering students' understanding of topics covered in MAT 153.

### Text

Precalculus: a Prelude to Calculus (1st ed.), by Sheldon Axler. Wiley, 2009.

#### Course Coverage

MAT 153 focuses on the following chapters in the text.

• 0. The Real Numbers
• 1. Functions and their Graphs
• 2. Linear, Quadratic, Polynomial, and Rational Functions
• 3. Exponentials, Logarithms, and e.
• 4. Trigonometric Functions
• 5. Trigonometric Algebra and Geometry.
• 6. Applications of Trigonometry

Students' grades are based on homework, class participation, short tests, and scheduled examinations covering students' understanding of the topics covered in MAT 153. The instructor determines the relative weights of these factors. Instructore are encouraged to allow the use of graphing calculators on tests and homework. Students may be allowed to use sheet of formulas (written by the student or provided by the instructor) during tests at the instructor's discretion.

### Attendance Requirements

Attendance policy is set by the instructor.

### Policy on Due Dates and Make-Up Work

Due dates and policy regarding make-up work are set by the instructor.

### Schedule of Examinations

The instructor sets all test dates except the date of the final exam. The final exam is given at the date and time announced in the Schedule of Classes.